I need to (at times) have our mail server pull email off of Dynu.com. At times we pull the main server offline for whatever reason and use a backup server at an unknown (beforehand) location. Since standard services (Frontier, Comcast, etc) put a firewall in the "modems" these days mail cannot come from the wild west (normal email traffic) onto the server as the firewall will block it. So to work around our servers can reach out and pull email off of other servers, then distribute them locally as normal. I see the Dynu.com services but I do not see any service that will allow us to grab mail off of Dynu.com when we need to. Any ideas?

This is low priority as it will only be used at random times but still a high priority when needed.

I don't think you can pull emails from the servers. Dynu servers will keep sending emails to your server until your server accepts them or remove the emails if they expire. The emails will expire once 4000 attempts have been made to deliver the email. How often the attempt is made is determined by the Retry (mins) you set up in the control panel.

If you want the emails to be sent immediately, you can reduce the retry interval.